Trading in CEXs and DEXs with Priority Fees and Stochastic Delays

TL;DR

This paper introduces a novel stochastic impulse control framework for optimal trading across centralized and decentralized exchanges, accounting for delays, costs, and priority fees, with implications for latency risk management.

Contribution

It extends impulse control models by incorporating stochastic delay choices and multiple pending orders, applied to optimal trading between CEXs and DEXs.

Findings

Optimal priority fee significantly improves trading performance.

Model provides insights into latency risk management strategies.

Mathematically derives dynamic programming principles for complex impulse controls.

Abstract

We develop a mixed control framework that combines absolutely continuous controls with impulse interventions subject to stochastic execution delays. The model extends current impulse control formulations by allowing (i) the controller to choose the mean of the stochastic delay of their impulses, and allowing (ii) for multiple pending orders, so that several impulses can be submitted and executed asynchronously at random times. The framework is motivated by an optimal trading problem between centralized (CEX) and decentralized (DEX) exchanges. In DEXs, traders control the distribution of the execution delay through the priority fee paid, introducing a fundamental trade-off between delays, uncertainty, and costs. We study the optimal trading problem of an agent exploiting trading signals in CEXs and DEXs. From a mathematical perspective, we derive the associated dynamic programming principle of this new class of impulse control problems, and establish the viscosity properties of the corresponding quasi-variational inequalities. From a financial perspective, our model provides insights on how to carry out execution across CEXs and DEXs, highlighting how traders manage latency risk optimally through priority fee selection. We show that employing the optimal priority fee has a significant outperformance over non-strategic fee selection.